ID-Based Series-Parallel Multisignature Schemes for Multi-Messages from Bilinear Maps

  • Lihua Wang
  • Eiji Okamoto
  • Ying Miao
  • Takeshi Okamoto
  • Hiroshi Doi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3969)


In this paper series-parallel multisignature schemes for multi-messages are investigated. We propose an ID-based series-parallel multisignature scheme (ID-SP-M4M scheme) based on pairings in which signers in the same subgroup sign the same message, and those in different subgroups sign different messages. Our new scheme is an improvement over the series-parallel multisignature schemes introduced by Doi, Mambo and Okamoto [5] and subsequent results such as the schemes proposed by Burmester et al. [4] and the original protocols proposed by Tada [17,18], in which only one message is to be signed. Our ID-SP-M4M scheme is secure against forgery signature attack from parallel insiders under the BDH assumption.


Elliptic Curf Signing Order Weil Pairing Tate Pairing Choose Message Attack 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Boneh, D., Franklin, M.: Identity-Based Encryption from the Weil Pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiably encrypted signatures from bilinear maps. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 416–432. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Boyd, C.: Digital multisignatures. In: Proc. IMA Conf. Crypto. Coding, pp. 241–246. Clarendon, Oxford (1989)Google Scholar
  4. 4.
    Burmester, M., Desmedt, Y.G., Doi, H., Mambo, M., Okamoto, E., Tada, M., Yoshifuji, Y.: A structured elGamal-type multisignature scheme. In: Imai, H., Zheng, Y. (eds.) PKC 2000. LNCS, vol. 1751, pp. 466–483. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Doi, H., Mambo, M., Okamoto, E.: Multisignature scheme with specified order. In: SCIS94-2A, Biwako, Japan (1994)Google Scholar
  6. 6.
    Doi, H., Mambo, M., Okamoto, E.: RSA-based multisignature scheme for various group structure. Journal of Information Processing Society of Japan 41(8), 2080–2091 (2000)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Doi, H., Mambo, M., Okamoto, E.: On the security of the RSA-based multisignature scheme for various group structures. In: Clark, A., Boyd, C., Dawson, E.P. (eds.) ACISP 2000. LNCS, vol. 1841, pp. 352–367. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM Journal on Computing 17(2), 281–308 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Joux, A.: The Weil and Tate pairings as building blocks for public key cryptosystems. In: Fieker, C., Kohel, D.R. (eds.) ANTS 2002. LNCS, vol. 2369, pp. 20–32. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Kawauchi, K., Komano, Y., Ohta, K., Tada, M.: Probabilistic multi-signature schemes using a one-way trapdoor permutation. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E87-A(5), 1141–1153 (2004)Google Scholar
  11. 11.
    Kawauchi, K., Minato, H., Miyaji, A., Tada, M.: A multi-signature scheme with signers’ intentions secure against active attacks. In: Kim, K.-c. (ed.) ICISC 2001. LNCS, vol. 2288, pp. 328–340. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    Barreto, P.S.L.M., Kim, H.Y., Lynn, B., Scott, M.: Efficient algorithms for pairing-based cryptosystems. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 354–368. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    Mitomi, S., Miyaji, A.: A general model of multisignature schemes with message flexibility, order flexibility, and order verifiability. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E84-A(10), 2488–2499 (2001)zbMATHGoogle Scholar
  14. 14.
    Ohta, K., Okamoto, T.: A digital multisignature scheme based on the Fiat-Shamir scheme. In: Matsumoto, T., Imai, H., Rivest, R.L. (eds.) ASIACRYPT 1991. LNCS, vol. 739, pp. 139–148. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  15. 15.
    Okamoto, T.: A digital multisignature scheme using bijective public-key cryptosystems. ACM Trans. Computer Systems 6, 432–441 (1988)CrossRefzbMATHGoogle Scholar
  16. 16.
    Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems based on pairing. In: SCIS2000-C20, Okinawa, Japan (2000)Google Scholar
  17. 17.
    Tada, M.: An order-specified multisignature scheme secure against active insider attacks. In: Batten, L.M., Seberry, J. (eds.) ACISP 2002. LNCS, vol. 2384, pp. 328–345. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Tada, M.: A secure multisignature scheme with signing order verifiability. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E86-A(1), 73–88 (2003)Google Scholar
  19. 19.
    Washington, L.C.: Elliptic Curves: Number Theory and Cryptography. Chapman & Hall/CRC, Boca Raton (2003)zbMATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Lihua Wang
    • 1
  • Eiji Okamoto
    • 1
  • Ying Miao
    • 1
  • Takeshi Okamoto
    • 1
  • Hiroshi Doi
    • 2
  1. 1.Graduate School of Systems and Information EngineeringUniversity of TsukubaTsukubaJapan
  2. 2.Graduate School of Information SecurityInstitute of Information SecurityYokohamaJapan

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